Super Fractional Brownian Motion, Fractional Super Brownian Motion and RelatedSelf-Similar (Super) Processes

摘要

We consider the full weak convergence, in appropriate function spaces, of systemsof noninteracting particles undergoing critical branching and following a self similar spatial motion with stationary increments. The limit processes are measure valued. and are of the super and historical process type. In the case in which the underlying motion is that of a fractional Brownian motion, we obtain a characterisation of the limit process as a kind of stochastic integral against the historical process of a Brownian motion defined on the full real line.